What Is The General Formula Of Sequence 0,2,6,12,20?
What is the general formula of sequence 0,2,6,12,20?
Answer:
Step-by-step explanation:
Examine the differences between successive elements to find:
a
n
=
n
2
+
n
s
n
=
1
3
n
(
n
+
1
)
(
n
+
2
)
Explanation:
Given the sequence
2
,
6
,
12
,
20
, write it out in a line with gaps between each term:
2
00000
6
00000
12
00000
20
Add a line of term below listing the differences between each pair of terms:
2
00000
6
00000
12
00000
20
000
4
00000
6
000000
8
Add another line of term below listing the differences between each pair of terms:
2
00000
6
00000
12
00000
20
000
4
00000
6
000000
8
000000
2
000000
2
Notice that both terms of the last line are the same.
That implies that our given sequence can be matched using a quadratic formula, which we can construct using the first term of each of the lines as a coefficient:
a
n
=
2
0
!
+
4
1
!
(
n
−
1
)
+
2
2
!
(
n
−
1
)
(
n
−
2
)
a
n
=
2
+
4
n
−
4
+
n
2
−
3
n
+
2
Comments
Post a Comment